1. Field of the Invention
The present invention relates to a shape measuring apparatus which measures the shape of an object to be measured by processing an output signal obtained when the object is scanned with a detector, and more particularly to a phase delay correction system which is capable of measuring the shape with high accuracy by concerning a phase delay which occurs in a signal process for processing a shape detection signal expressed in a Fourier series.
2. Prior Art
In an accurate shape measurement of the object to be measured, such as a measurement of the surface roughness, the three-dimensional shape or objects similar in shape and roughness, a relative scan of the object is performed using a contact or non-contact type detector, thereby obtaining a shape detection signal as a position function, and this detection signal is processed. When a predetermined spatial range around the object is scanned at a constant speed, the detection signal is output from the detector as a time function. Generally, this detection signal is sampled and converted to digital data. The digital data is then processed by a computer for use in a shape measurement. In this digital processing, the detection signal is expressed in the form of a Fourier series whose components include a spatial phase component corresponding to a spatial position.
In the shape detection data expressed in a Fourier series, as the order of the Fourier series is increased in a range wherein a noise against a true value can be controlled, the precision with which shape detection data represents the shape of the object in the scanned spatial range is improved. Therefore, in recent years, the order of the Fourier series (that is, the order of a spatial harmonic component) has been increased more and more to reproduce the shape of the object with high reproducibility, and a demand for an order higher than the 500th order has also become remarkable.
In a signal processing procedure for converting a signal output from the shape detector to digital data and processing the data in the form of a Fourier series, a large number of noises enter into the signal. These noises include a noise entering from the outside of the shape detector, a quantization error noise generated in the process of converting an analog signal output from the detector to a digital signal, and a noise due to a switching operation of an electric circuit. A filter for taking out components having frequencies within a predetermined range is generally used for the purpose of suppressing these noises. The filter may be arranged in an analog circuit, or a digital filter may be employed if the signal is digitized.
In the case where the shape detection data is processed through the digital filter as described above, a phase difference between the input and output of the filter is observed depending on the filter characteristics. The phase difference between the input and the output is added to a phase delay in the signal transmitted from the detector. This phase delay causes a "distortion" of the shape and a "mechanical positional deviation" when the shape of the object to be measured is reproduce. Thus, a reduction in the "distortion" and the "mechanical positional deviation" has been the subject to be achieved for measuring the shape of the object with high accuracy.
Conventionally, some methods for preventing the above-described "distortion" have been proposed, while no methods have been proposed for preventing the "mechanical positional deviation". However, a technique for preventing the "distortion" sometimes causes a considerable "mechanical positional deviation". In the case where a bi-directional relative scan, not a unidirectional relative scan, is performed for the purpose of a time reduction, the "mechanical positional deviation" causes a hysteresis error in the reproduced shape. Besides, this error becomes remarkable proportionally as the scanning speed is increased.
The mechanical positional deviation caused by the phase delay will now be explained more in detail. For instance, let it be considered the case where the scanning width for the object to be measured is 100 mm, the object is scanned at a speed of 100 mm/sec and detection data is obtained with a spatial frequency of 500 Hz (that is, the maximum measurement order is 500). In this case, provided that the digital filter has a linear phase characteristic and the angle of the phase delay is 90 degrees at a spatial frequency of 500 Hz, for example, the mechanical positional deviation of the object from the origin (the scanning reference position) is estimated as (100 mm/500).times.(90.degree./360.degree.)=50 .mu.m in case of the maximum measurement order. If the scan is bi-directional, the hysteresis error calculated in terms of mechanical position will be 2.times.50 .mu.m=100 .mu.m.
If the object to be measured is processed with an ordinary machine tool of a numerical control type and the control level of the numerical control system is 0.1 to 1 m in the processing accuracy, the above-described positional deviation and the postional hysteresis error will be unallowable.
As explained above, the phase delay which occurs during the signal processing causes the positional deviation of the object from the origin when the detector is moved relative to the object at a constant speed. Further, the deviation of the phase characteristic from the linear phase characteristic causes the distortion of the shape which is reproduced from the detection data.
The effects of the phase delay depends on the characteristics of the inserted filter. For example, a Butterworth filter which is used quite often is a recursive filter whose elements and parameters necessary to attain the desired attenuation are small in number. However, the recursive filter is not so preferable in terms of its phase characteristics. FIG. 4 is a diagram showing a step response in a Butterworth communication function (cited from "Linear Control System Analysis and Design" authored by D'Azzo Houpis). Referring to the eighth-order step response, it can be understood that the response is quite different from the simplest linear phase characteristic.
For the purpose of preventing only the "distortion" of the shape caused by the deviation of the phase characteristic of the digital filter from the linear phase characteristic, a filter having the linear phase characteristic, that is, a non-recursive filter, can be employed. The non-recursive filter can be realized by arranging the design of the calculation processing section of the digital filter.
When the non-recursive filter is adopted to realize the desired noise suppressing characteristic, the amount of phase delay becomes quite large, and accordingly an increase occurs in the mechanical positional deviation.
In the case where the detection data regarding the shape of the object and including the position data from the origin is stored prior to data processing for the restoration of the shape and there is no time limitations in the data processing, the bi-directional filtering system which is capable of eliminating the effects of the phase delay is efficient. However, this filter can be adopted under the condition in which all data regarding the shape are stored prior to the data processing. Further, those data all involve the position data from the origin which serves as a detection reference point, in consideration of the mechanical positional deviation. Due to this, the amount of data is considerably large. Such a condition may not always be satisfied, and the processing takes a long time because of the large amount of data. Therefore, the above filter is not suitable for use in high speed processing for measuring the shape of the object simultaneously with a machining process in real time, for example.
As explained above, when the shape detecting signal, obtained by scanning the object to be measured with the detector, is processed as data expressed in a Fourier series in order to restore the shape of the object, the phase delay during the signal processing has been a problematic matter which causes the distortion of the shape and the mechanical positional deviation of the object.